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János Kollár - Families of Varieties of General Type, Inbunden

Inbunden, Engelska, 2023

Families of Varieties of General Type

Av János Kollár

Del 231 i serien Cambridge Tracts in Mathematics

2329 kr

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Beskrivning
This book establishes the moduli theory of stable varieties, giving the optimal approach to understanding families of varieties of general type. Starting from the Deligne-Mumford theory of the moduli of curves and using Mori's program as a main tool, the book develops the techniques necessary for a theory in all dimensions. The main results give all the expected general properties, including a projective coarse moduli space. A wealth of previously unpublished material is also featured, including Chapter 5 on numerical flatness criteria, Chapter 7 on K-flatness, and Chapter 9 on hulls and husks.
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János Kollár is Professor of Mathematics at Princeton University. He has received the Cole Prize (2006), the Nemmers Prize (2016), and the Shaw Prize (2017). He is the author of more than 200 articles and ten books, mostly on algebraic geometry.

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'This book dismantles the final, most daunting barriers to learning about moduli of higher dimensional varieties, from the point of view of the Minimal Model Program. The first chapter draws the reader in with a compelling history; a discussion of the main ideas; a visitor's trail through the subject, complete with guardrails around the most dangerous traps; and a rundown of the issues that one must overcome. The text that follows is the outcome of Kollár's monumental three-decades-long effort, with the final stones laid just in the last few years.' Dan Abramovich, Brown University

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